BCX-24 will be given to patients with cutaneous T-cell lymphoma (CTCL). Part B consists of doses for patients at the seventh, eight, and ninth dosing levels. The total daily dose for these levels is as follows: 7th-216mg/m2, 8th -288mg/m2 and 9th -383mg/m2 this represents an increase of 33% over the previous dose levels. The patients will receive the study drug for 28 consecutive and have a 14 day washout period before evaluation and determination is made to begin cycle 2. They will be monitored carefully by blood and urine samples that will be collected every other week when the patient is scheduled for an evaluation visit and tested off sight at a laboratory as per protocol. Patients have reported on the study drug that they have experienced some headaches, nausea and vomiting. Medications will be given to alleviate any discomfort. Patients should be asked to keep track of the changes and monitor the noticeable side effects so that they can report them to study staff and recorded in their chart.